Back in January 2014, Bing enabled https support on their main website. Great news, and everyone should be using this as their default home page. However the search bar and location bar still use a non-secure http version of Bing which means adhoc searches are public.

I have placed an xml file to install a SSL version of the Bing search and you can install it by clicking here:

A text version can be displayed clicking here for those of you wondering what is in the file! Basically it is the default Bing provider with http changed to https and the name changed so as to not conflict.